Projected Climate Change Impacts on the Number of Dry and Very Heavy Precipitation Days by Century’s End: A Case Study of Iran’s Metropolises

Abstract

This study explores the impacts of climate change on the number of dry days and very heavy precipitation days within Iran’s metropolises. Focusing on Tehran, Mashhad, Isfahan, Karaj, Shiraz, and Tabriz, the research utilizes the sixth phase of the Coupled Model Intercomparison Project (CMIP6) Global Circulation Models (GCMs) to predict future precipitation conditions under various Shared Socioeconomic Pathways (SSPs) from 2025 to 2100. The study aims to provide a comprehensive understanding of how climate change will affect precipitation patterns in these major cities. Findings indicate that the SSP126 scenario typically results in the highest number of dry days, suggesting that under lower emission scenarios, precipitation events will become less frequent but more intense. Conversely, SSP585 generally leads to the lowest number of dry days. Higher emission scenarios (SSP370, SSP585) consistently show an increase in the number of very heavy precipitation days across all cities, indicating a trend towards more extreme weather events as emissions rise. These insights are crucial for urban planners, policymakers, and stakeholders in developing effective adaptation and mitigation strategies to address anticipated climatic changes.

1. Introduction

The study of precipitation patterns is essential for understanding the broader implications of climate change, particularly in regions with diverse climatic conditions like Iran [1]. One of the key indicators of climate variability is the number of dry days. Future changes in the annual count of dry days may either amplify or mitigate the anticipated rise in daily rainfall intensity due to climate warming [2]. The nation’s long-term average annual rainfall is approximately 252 mm, which is only one-third of the global average. In contrast, the average evaporation rate exceeds 179 mm, accounting for 71% of the country’s total precipitation, three times the global rate. In this environment, the prevalence of dry days significantly impacts water availability, agricultural productivity, and urban water supply systems, all of which are essential to local livelihoods [1].

Conversely, the number of very heavy precipitation days is equally significant, as these events can lead to severe flooding, soil erosion, and damage to infrastructure [3]. This dual focus on dry and heavy precipitation days provides a comprehensive understanding of the extremes in precipitation patterns and their potential impacts on Iran’s metropolises.

Iran, characterized by its arid and semi-arid climate, has witnessed significant shifts in its precipitation patterns over recent decades, largely due to the impacts of climate change. These climatic changes have led to an increase in both the frequency and intensity of dry days and very heavy precipitation days [4]. The metropolises of Iran, including Tehran, Mashhad, Isfahan, Karaj, Shiraz, and Tabriz, are particularly vulnerable to these changes due to their high population densities and extensive urban development. Analyzing trends in precipitation extremes is essential for these cities to develop effective water management strategies and enhance urban resilience against climate-induced hazards. This is particularly important in Iran, where mismanagement of water resources, adverse weather, and challenging geographical conditions pose significant challenges [5].

Previous studies have extensively documented the trends in precipitation extremes in Iran, offering valuable insights and methodologies to understand their dynamics and implications. These studies have utilized a range of approaches, from statistical analyses to modeling techniques, to capture the complexities of climate change impacts on precipitation. Below is a list of studies, detailing their methodologies and key findings:

Rahimzadeh et al. (2009) analyzed the variability of extreme temperatures and precipitation in Iran over recent decades. Using statistical analysis of observational data, they identified significant trends in both temperature and precipitation extremes, contributing to the understanding of regional climate variability [6]. Modarres and Sarhadi (2009) performed a trend analysis of rainfall data from the last half of the twentieth century. They applied statistical methods to detect changes in rainfall patterns, providing evidence of shifting precipitation regimes and their potential impacts on water resources [7]. Tabari et al. (2011) studied the trends in annual maximum, minimum, and mean air temperatures and precipitation in the west, south, and southwest of Iran from 1966 to 2005. They found a warming trend in annual Tmean, Tmax, and Tmin at most stations, beginning in the 1970s, with significant positive trends averaging +0.412, +0.452, and +0.493 °C per decade, respectively. However, precipitation trends were not uniform, showing both increasing and decreasing patterns across the region. [8]. Khalili et al. (2013) applied hydrological modeling to assess the vulnerability of urban areas to extreme weather events. Their research focused on the impacts of heavy rainfall on urban infrastructure and the effectiveness of flood management practices. The study revealed significant vulnerabilities in urban areas, highlighting the need for enhanced urban planning and flood mitigation measures [9]. Raziei et al. (2013) studied the spatial patterns and temporal trends in precipitation in Iran from 1951 to 2009 using the Global Precipitation Climatology Centre dataset. They found that precipitation patterns are influenced by orography and latitude, with distinct differences between arid and mountainous regions. While trends indicate increasing precipitation in autumn and winter and decreasing precipitation in spring and summer, these trends are not statistically significant in most areas [10]. Farajzadeh et al. (2014) employed optimization techniques to develop water allocation strategies under different climate scenarios. This study addressed the challenges of water shortages during prolonged dry periods and provided a framework for optimizing water use to minimize shortages, which is critical for sustainable water management in arid regions [11]. Balling Jr. et al. (2016) used trend analysis to investigate long-term changes in precipitation patterns, finding significant shifts towards more extreme precipitation events [12]. Khosravi et al. (2017) utilized satellite data and remote sensing techniques to monitor and predict drought conditions, offering valuable tools for early warning systems [13]. Shokouhi et al. (2018) applied climate models to simulate future precipitation scenarios under various greenhouse gas emission pathways, providing insights into how different mitigation strategies could influence future precipitation extremes [14]. Ghiami-Shamami et al. (2019) conducted a spatial analysis of precipitation extremes, identifying regional hotspots of vulnerability and proposing targeted adaptation measures [15]. Aghapour Sabbaghi et al. (2020) integrated socio-economic data with climate projections to assess the combined impacts of climate change and socio-economic factors on water resources, highlighting the importance of multi-faceted approaches to climate adaptation [16]. More recently, Mahbod et al. (2023) analyzed the spatial and temporal variations of wet and dry spells in Iran from 1985 to 2016 using 14 indices from 512 rain gauges. They found that wet spells have declined in southern Iran but expanded in the north, with extreme wet spells intensifying nationwide. Their study also revealed that El Niño events lead to wetter conditions in Iran, and long-term Pacific sea-surface temperature oscillations are significantly correlated with wet/dry spells [17]. In another study, Zarrin and Dadashi-Roudbari (2024) assessed mean precipitation and extremes in Iran using the RegCM4 model over a 20-year period (1991–2010) with a 20 km resolution. They found that the model reasonably captured precipitation patterns and extremes, despite biases in the northwest and southeast due to convection and monsoon precipitation, respectively. Their results indicated a general decrease in precipitation and an increase in consecutive dry days (CDD), especially in the southeast, highlighting a trend towards drier conditions in the 2000s compared to the 1990s [18].

This study aims to analyze the impact of climate change on the cumulative number of dry days and very heavy precipitation days in Iran’s metropolises from 2025 to 2100. By examining historical precipitation data and 35 GCM simulations from the sixth phase of the CMIP6 series, we selected the most accurate GCMs to identify cities that are more prone to extreme precipitation events. This approach not only enhances the precision of climate projections but also provides a robust basis for understanding future precipitation patterns.

The novelty of this study lies in its comprehensive and integrative methodology, which combines historical data analysis with advanced climate modeling to provide a nuanced understanding of precipitation extremes. Unlike previous studies, which often focused on single aspects of precipitation variability, this research simultaneously addresses both dry days and very heavy precipitation days, offering a holistic view of climate impacts. Moreover, in the context of Iran’s metropolises, very limited studies have specifically focused on these two extreme conditions, and have utilized the latest CMIP6 GCMs and SSP scenarios to project future climate impacts. Additionally, this study bridges the gap between scientific research and practical policy-making, offering actionable insights for enhancing urban resilience and sustainable development. The findings of this research will be instrumental in guiding policy decisions and formulating adaptive strategies to address the challenges posed by changing precipitation patterns in the context of a warming climate. Previous research has laid the groundwork for this analysis, highlighting the importance of regional studies to capture the unique climatic characteristics of different areas. Therefore, understanding the dynamics of these precipitation extremes is vital for policymakers and urban planners to mitigate their adverse effects and ensure sustainable development in Iran’s metropolises.

2. Materials and Methods

2.1. Iran’s Metropolises and Data Sources

Spanning a vast geographical area, Iran encompasses a diverse range of climatic conditions. The country’s climate varies from the dry central deserts to the humid subtropical regions along the Caspian Sea, showcasing its extensive climatic diversity [19]. This study focuses on six major cities, each with its own unique climate: Tehran, Mashhad, Isfahan, Karaj, Shiraz, and Tabriz (Table 1). The distinct climates of these urban centers reflect the diverse climatic conditions found across Iran, influenced by its varied topography and geographic positioning. The locations of these cities, along with the climatic zones of Iran, are depicted in Figure 1.

Daily precipitation data were obtained from the Islamic Republic of Iran Meteorological Organization [20]. The records span from 1951 to 2023 for Tehran, Mashhad, Isfahan, Shiraz, and Tabriz, and from 1985 to 2023 for Karaj, based on data availability.

Table 1. The population and climate conditions of the case studies [21].

City	Population (Million)	Climate
Tehran	7.15	Situated in northern Iran, Tehran experiences a cold, semi-arid climate. The city lies at the foothills of the Alborz Mountains, which shield it from the harsher weather found in Iran’s interior. Summers in Tehran are usually hot and dry, with temperatures often exceeding 35 °C. Winters are relatively mild, although temperatures can sometimes drop below freezing. Most of Tehran’s precipitation occurs in the winter, primarily as rain, with snowfall also common.
Mashhad	2.31	Mashhad, located in northeastern Iran, has a cold, semi-arid climate. Positioned on a plateau and encircled by mountains, the city’s climate is influenced by its altitude and closeness to desert regions. Summers in Mashhad are typically hot, with temperatures often surpassing 35 °C. Conversely, winters are cold, with temperatures occasionally falling below freezing and frequent snowfall during the winter season.
Isfahan	1.55	Isfahan, located in central Iran, experiences a cold desert climate. The city is located on a large, dry plain encircled by mountains, resulting in extreme weather conditions. Summers in Isfahan are intensely hot, with temperatures frequently rising above 40 °C. On the other hand, winters are relatively mild, though temperatures can occasionally drop below freezing. Precipitation is scarce throughout the year, with the majority occurring during the winter months.
Karaj	1.45	Situated northwest of Tehran, Karaj has a climate similar to the nearby capital. Nestled on the lower slopes of the Alborz Mountains, the city experiences a cold, semi-arid climate. Summers in Karaj are hot and dry, whereas winters are cool and wet, with occasional snowfall. The majority of the annual precipitation falls in the winter, mainly as rain.
Tabriz	1.42	Located in northwestern Iran, Tabriz experiences a humid continental climate. Tabriz’s climate is heavily influenced by its position at the base of the Sahand Mountains and its closeness to the Caspian Sea. Summers in Tabriz are warm and dry, whereas winters are cold and snowy, with temperatures often falling below freezing. The majority of the city’s precipitation occurs during the winter, primarily as snow.
Shiraz	1.25	Situated in southwestern Iran, Shiraz has a cold, semi-arid climate. The city’s weather is influenced by its position on a plateau encircled by the Zagros Mountains. Summers in Shiraz are typically hot and dry, with temperatures frequently exceeding 35 °C. Winters are mild, with temperatures seldom falling below freezing. Most of the city’s annual precipitation occurs during the winter months, mainly as rain.

Table 1. The population and climate conditions of the case studies [21].

City	Population (Million)	Climate
Tehran	7.15	Situated in northern Iran, Tehran experiences a cold, semi-arid climate. The city lies at the foothills of the Alborz Mountains, which shield it from the harsher weather found in Iran’s interior. Summers in Tehran are usually hot and dry, with temperatures often exceeding 35 °C. Winters are relatively mild, although temperatures can sometimes drop below freezing. Most of Tehran’s precipitation occurs in the winter, primarily as rain, with snowfall also common.
Mashhad	2.31	Mashhad, located in northeastern Iran, has a cold, semi-arid climate. Positioned on a plateau and encircled by mountains, the city’s climate is influenced by its altitude and closeness to desert regions. Summers in Mashhad are typically hot, with temperatures often surpassing 35 °C. Conversely, winters are cold, with temperatures occasionally falling below freezing and frequent snowfall during the winter season.
Isfahan	1.55	Isfahan, located in central Iran, experiences a cold desert climate. The city is located on a large, dry plain encircled by mountains, resulting in extreme weather conditions. Summers in Isfahan are intensely hot, with temperatures frequently rising above 40 °C. On the other hand, winters are relatively mild, though temperatures can occasionally drop below freezing. Precipitation is scarce throughout the year, with the majority occurring during the winter months.
Karaj	1.45	Situated northwest of Tehran, Karaj has a climate similar to the nearby capital. Nestled on the lower slopes of the Alborz Mountains, the city experiences a cold, semi-arid climate. Summers in Karaj are hot and dry, whereas winters are cool and wet, with occasional snowfall. The majority of the annual precipitation falls in the winter, mainly as rain.
Tabriz	1.42	Located in northwestern Iran, Tabriz experiences a humid continental climate. Tabriz’s climate is heavily influenced by its position at the base of the Sahand Mountains and its closeness to the Caspian Sea. Summers in Tabriz are warm and dry, whereas winters are cold and snowy, with temperatures often falling below freezing. The majority of the city’s precipitation occurs during the winter, primarily as snow.
Shiraz	1.25	Situated in southwestern Iran, Shiraz has a cold, semi-arid climate. The city’s weather is influenced by its position on a plateau encircled by the Zagros Mountains. Summers in Shiraz are typically hot and dry, with temperatures frequently exceeding 35 °C. Winters are mild, with temperatures seldom falling below freezing. Most of the city’s annual precipitation occurs during the winter months, mainly as rain.

2.2. GCMs and Climate Change Scenarios

GCMs are crucial for predicting future climate conditions under different emission scenarios. These models are widely acknowledged for their extensive applicability in various contexts [22], but they also display varying degrees of accuracy across different climate variables and geographic regions. The variability in GCM performance highlights their complex nature, necessitating careful analysis and use of their outputs for reliable climate projections.

This study employed 35 GCM simulations from the CMIP6. High-resolution, bias-adjusted, and downscaled climate projections were obtained from the NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP-CMIP6) portal [23]. The GCM projections, provided in NetCDF format, were extracted for specific geographic locations.

Shared Socioeconomic Pathways (SSPs) are a set of climate change scenarios that project global socioeconomic developments until the year 2100. These pathways are central to creating greenhouse gas emission scenarios that correspond with different climate policy frameworks. The SSPs describe a range of potential future socio-economic developments through narratives that provide both qualitative and quantitative elements. These narratives offer detailed, interconnected descriptions of possible futures while also incorporating quantitative projections related to demographic changes, urban development, and economic growth, such as GDP per capita [24].

Table 2. The SSP scenarios employed in this study.

Scenario	Description	Example Studies	Key Findings
SSP126	The SSP126 scenario aims to simulate a development compatible with the 2 °C target. It is a remake of the optimistic RCP2.6 scenario, assuming climate protection measures are taken. By the year 2100, it reaches a radiative forcing level of 2.6 W/m².	- Zhou et al. (2023) evaluated increased global concurrent climate extremes due to anthropogenic climate forcing [25]. - Reddy et al. (2023) studied the effects of climate change on streamflow in the Godavari Basin, India, using a conceptual model including the CMIP6 dataset [26]. - Kamal et al. (2021) analyzed the spatiotemporal changes in rainfall and droughts of Bangladesh using the CMIP6 models [27].	- Zhou et al. (2023) discovered that SSP126 significantly mitigates the future intensification of concurrent climate extremes, especially in high-risk tropical and northern high-latitude regions. - Reddy et al. (2023) reported that the SSP126 scenario generally predicts decreases in seasonal streamflow during winter and pre-monsoon periods, but significant increases in annual streamflow. Additionally, rainfall and temperatures are projected to increase moderately in the future. - Kamal et al. (2021) reported that although future climate extremes will increase compared to historical conditions, the ambitious emissions mitigation pathway of SSP126 will significantly moderate the future intensification of these extremes.
SSP245	The SSP245 scenario, an update to the RCP4.5 scenario, represents the medium pathway for future greenhouse gas emissions. By the year 2100, it reaches an additional radiative forcing of 4.5 W/m². This scenario assumes that climate protection measures are being taken, but it does not achieve net-zero emissions by 2100.	- Goodarzi et al. (2024) investigated the uncertainty of future predictions of temperature and precipitation in the Kerman Plain under climate change impacts [28]. - Wang et al. (2022) analyzed the characteristics and projections of meteorological drought in the Yellow River Basin, China, using GCMs and Standardized Precipitation-Evapotranspiration Index (SPEI) indicators from 2015 to 2100 [29]. - Zhang et al. (2022) proposed a novel statistical downscaling approach for analyzing daily precipitation and extremes under the impact of climate change in the Amu Darya River basin, Central Asia [30].	- Goodarzi et al. (2024) reported that under the SSP245 scenario, the average temperature in the Kerman Plain is projected to increase by approximately 1.5 °C from 2023 to 2054. However, precipitation predictions show mixed results. - Wang et al. (2022) found that under the SSP245 scenario, the characteristics of meteorological drought in the Yellow River Basin are projected to intensify from 2040 to 2099. The study indicated that the intensity and frequency of droughts are likely to increase, particularly in the Loess Plateau and the main water conservation areas of the Yellow River Basin. - Zhang et al. (2022) reported that under the SSP245 scenario, mean precipitation values are projected to increase by 56 ± 41 mm per year. Additionally, both average precipitation levels and extreme precipitation events are expected to rise throughout the 21st century.
SSP370	The SSP370 scenario represents an upper-middle pathway for future greenhouse gas emissions. By the year 2100, it reaches a radiative forcing level of 7 W/m². SSP370 was introduced after the RCP scenarios, bridging the gap between RCP6.0 and RCP8.5.	- Kamruzzaman et al. (2023) predicted the changes in future precipitation and air temperature across Bangladesh using CMIP6 GCMs [31]. - Xiang et al. (2022) evaluated the impact of climate change on the hydrological regime of the Yarkant River Basin, China [32]. - Jin et al. (2021) studied the spatio-temporal changes in precipitation in the Hanjiang River Basin, China, under climate change [33].	- Kamruzzaman et al. (2023) reported that under the SSP370 scenario, winter precipitation is predicted to decrease the most, by 11.12%, in the mid-future period (2045–2074). - Xiang et al. (2022) reported a significant increase in temperature and precipitation across three SSP scenarios, leading to a projected rise in streamflow, particularly during summer and winter. - Jin et al. (2021) found that under the SSP370 scenario, total precipitation in the Hanjiang River Basin is projected to show an increasing trend.
SSP585	The SSP585 scenario, also known as “Fossil-fueled Development,” represents an upper boundary in terms of greenhouse gas emissions. By the year 2100, it reaches an additional radiative forcing of 8.5 W/m². In this scenario, global markets are highly integrated, leading to technological progress and innovation.	- Reddy and Saravanan (2023) studied the extreme precipitation indices over India using CMIP6 [34]. - Bian et al. (2021) projected the hydrological responses to climate change using CMIP6 climate scenarios for the Upper Huai River Basin, China [35]. - Piao et al. (2021) investigated future projections of precipitation, surface temperatures, and drought events over the monsoon transitional zone in China from bias-corrected CMIP6 models [36].	- Reddy and Saravanan (2023) reported that the SSP585 scenario predicts significant increases in temporal variation, with heavy precipitation rising by about 45.41%, very heavy precipitation by 149.40%, maximum 1-day precipitation by 52.26%, and maximum 5-day precipitation by 45.92% compared to the current climate. - Bian et al. (2021) report that while future precipitation trends show insignificant increases, temperatures are projected to rise significantly. Under the SSP585 scenario, average monthly runoffs are expected to decrease during the low-flow season in the 2050s and increase during the high-flow season in the 2080s. Design floods with return periods below 50 years are projected to decrease during the 2050s but show a significant increasing trend in the 2080s, especially for longer return periods, indicating more severe future flood events. - Piao et al. (2021) predict that the monsoon transitional zone will become increasingly dry in future periods due to a significant rise in semiarid events and a decrease in humid events. The study highlights that under the SSP585 scenario, drought conditions will develop more rapidly compared to other scenarios, with similar frequencies of wet and dry events in the long term.

presents the details of the scenarios utilized in this study, along with examples of studies by other researchers and their key findings.

2.3. Dry Days and Very Heavy Precipitation Days

The Expert Team on Climate Change Detection and Indices (ETCCDI) has developed and standardized a suite of climate indices to characterize changes in extreme weather and climate events, particularly rainfall. The ETCCDI’s standardized indices help in understanding and comparing rainfall extremes across different regions globally [37].

According to ETCCDI, dry days are defined as those with less than 1 mm of rainfall. The occurrence of dry days significantly impacts water cycles, natural ecosystems, and human endeavors such as farming, tourism, and transportation. With rising global temperatures, the number of dry days is expected to increase notably in various areas, especially in subtropical and Mediterranean regions [2].

On the other hand, very heavy precipitation days are defined as those whose precipitation exceeds 20 mm. These extreme precipitation events can lead to localized flooding, particularly in urban or steep terrains where runoff is rapid and drainage systems may be overwhelmed [38].

2.4. Statistical Methods

2.4.1. Augmented Dickey–Fuller (ADF) Test

The ADF test is a widely used statistical method to determine whether a given time series is stationary. It falls under the category of unit root tests, which are the standard approach for testing the stationarity of a time series. A unit root, if present in a time series, indicates non-stationarity [39]. This is represented as:

$$Y_t=\alpha Y_{t-1}+\beta X_e+ϵ$$

(1)

where Y_t is the value of the time series at time t, X_e is an exogenous variable, and ϵ is the error term. The presence of a unit root implies that α = 1. To make the series stationary, the number of differencing operations corresponds to the number of unit roots present.

The Dickey–Fuller test, a unit root test, evaluates the null hypothesis H₀: α = 1 using Equation (2).

$$y_t=c+\beta t+\alpha y_{t-1}+\phi \Delta Y_{t-1}+e_t$$

(2)

where y_t−1 is the lagged value, and ΔY_t−1 is the first difference in the series at time t − 1. If the null hypothesis is not rejected, the series is considered non-stationary.

The ADF test, an extension of the Dickey–Fuller test, incorporates higher-order autoregressive processes to enhance the robustness of the model. The ADF test equation is:

$$y_t=c+\beta t+\alpha y_{t-1}+{\phi }_1\Delta Y_{t-1}+{\phi }_2\Delta Y_{t-2}+\dots +{\phi }_p\Delta Y_{t-p}+e_t$$

(3)

This extended version includes multiple lagged differencing terms, making the test more comprehensive [40]. The null hypothesis remains H₀: α = 1. For the time series to be deemed stationary, the p-value of the test must be less than the chosen significance level (typically 0.05), leading to the rejection of the null hypothesis.

2.4.2. Mann–Kendall (MK) Trend Analysis

The MK trend test, introduced by Mann in 1945 [41] and later enhanced by Kendall in 1975 [42], is a flexible, non-parametric method applicable to diverse data distributions. This test is designed to detect monotonic upward or downward trends within time series data [43]. A notable advantage of the MK method is its independence from the distributional properties of the data, making it resistant to the influence of outliers and non-normal distributions [44,45]. Its robustness in the face of such anomalies has made it a favored tool for evaluating trends in hydrometeorological datasets. For a given time series {X_i, i = 1, 2, …, n}, the null hypothesis H₀ assumes it is independently distributed, and the alternative hypothesis H₁ is that there exists a monotonic trend. The test statistic S is given by:

$$S={\displaystyle \sum }_{i=1}^{n-1}{\displaystyle \sum }_{j=i+1}^{n}sgn\left(x_j-x_i\right)$$

(4)

where X_i and X_j are the values of sequences i and j; n is the length of the time series. Assuming ($x_j-x_i)=\theta$, the value of sgn($\theta$), and the variance are computed as:

$$sgn\left(\theta \right)=\left\{\begin{array}{c}+1 if \theta >0\\ 0 if \theta =0\\ -1 if \theta <0\end{array}\right.$$

(5)

$$var\left(s\right)={\displaystyle \frac{n\left(n-1\right)\left(2n+5\right)-{\sum }_{i=1}^m{T}_{i}i\left(i-1\right)\left(2i+5\right)}{18}}$$

(6)

where T_i is the number of data points in the tied group and m is the number of groups of tied ranks. The standardized test statistic Z is computed by:

$$Z=\left\{\begin{array}{c}{\displaystyle \frac{S-1}{\sqrt{var\left(S\right)}}} if S>0\\ 0 if S=0\\ {\displaystyle \frac{S+1}{\sqrt{var\left(S\right)}}} if S<0\end{array}\right.$$

(7)

Positive Z values indicate upward trends, whereas negative Z values signify downward trends. Trend significance is assessed at a selected α significance level. The null hypothesis is rejected if |Z| exceeds |$Z_{1-{\displaystyle \frac{\alpha }{2}}}$| for a two-tailed test or |Z| exceeds |$Z_{1-\alpha }$| for a one-tailed test, indicating a statistically significant trend in the time series. In this analysis, the null hypothesis was evaluated at a 95% confidence level, which is a standard significance level commonly used in statistical assessments [46,47].

2.4.3. Nash–Sutcliffe and Modified Nash–Sutcliffe Model Efficiency Coefficient

The NS model efficiency coefficient is a normalized statistic that measures the proportion of residual variance, representing ‘noise’, relative to the variance of the observed data, denoted as ‘information’ [48]. The NS assesses how well the plot of observed versus simulated data aligns with the 1:1 line (Equation (5)). Conversely, the MNS model efficiency coefficient offers enhanced sensitivity for detecting significant over- or under-predictions compared to the traditional NS coefficient. This enhancement is particularly effective when the parameter j equals 1, significantly reducing the overestimation of peak values [49]. This adjustment, introduced by Krause and colleagues, is crucial for improving our understanding of predictive accuracy, especially in complex forecasting scenarios with high model uncertainties. By incorporating the parameter j within the MNS formulation, a more detailed and accurate evaluation of model performance is achieved (Equation (6)).

$$NS=1-{\displaystyle \frac{{\sum }_i{\left(y_i-{\widehat{y}}_i\right)}^2}{{\sum }_i{\left(y_i-\overline{y}\right)}^2}}$$

(8)

$$MNS=1-{\displaystyle \frac{{\sum }_i{\left|y_i-{\widehat{y}}_i\right|}^j}{{\sum }_i{\left|y_i-\overline{y}\right|}^j}}$$

(9)

In this context, y_i and $\widehat{y}$ represent the observed and simulated variables, respectively; the bar indicates the average, and i is the ith measured or simulated value. The NS and MNS functions range from negative infinity to 1, with a score of 1 indicating a perfect alignment between the model’s predictions and the actual observed data. Values between 0 and 1 suggest a close match between simulated and observed values, while values below 0 imply that the model’s predictions fail to accurately reflect the observed data.

3. Results and Discussion

Iran, being the Middle East’s leading emitter and the world’s seventh-largest producer of greenhouse gasses, has substantial emissions primarily due to its large-scale oil and gas production and consumption. Additionally, the country’s swift urban growth has further compounded its emission levels [50]. Figure 2 depicts the progression of precipitation trends in recent decades in Iran’s metropolises. The blue lines represent the observed annual precipitation data, while the red dashed lines indicate the fitted polynomial trend lines, showing the general trend over the period. The equations of the trend lines are provided in each plot. According to Figure 2, in Tehran, the general trend shows variability, with a slight downward trend in recent years. Rapid urbanization and the resulting urban heat island effect have likely contributed to this trend. The changes in land use and reduction in vegetation cover in and around Tehran have also impacted local weather patterns, reducing the overall precipitation [51].

In Mashhad, the trend suggests a slight increase in precipitation initially, followed by a downward trend in recent decades. The city’s urbanization and local geographic features, including its elevation and proximity to mountainous regions, contribute to the observed precipitation patterns. The city’s development has likely influenced local weather [52], but the impact appears less pronounced compared to other metropolises.

In Isfahan, the trend shows a decrease in precipitation over the decades. The rapid urbanization of Isfahan has likely contributed to changes in local weather patterns. Urban heat islands, changes in land use, and vegetation cover have influenced precipitation trends [53].

In Karaj, the trend is relatively flat with minor fluctuations, indicating no significant long-term change. The rapid urban expansion and changes in land use have influenced the local climate, contributing to the observed trends. Karaj’s proximity to Tehran also means it shares similar climatic influences and urbanization impacts [54].

In Tabriz, the trend shows variability, with an overall slight downward trend in recent years. The city’s unique geographic location and elevation, along with its semi-arid climate, contribute to this pattern. Urbanization and land use changes in Tabriz have influenced local weather, but the impact appears to be moderate [55].

In Shiraz, there is a noticeable decline in precipitation over the observed period. The city has experienced several extreme weather events and unusual climatic phenomena in recent years [56]. The abnormal precipitation behavior in Shiraz is likely a combination of climatic factors and local geographic and urbanization impacts. Another factor that impacts southern areas of Iran, including Shiraz, is the El Niño and La Niña phenomena, which can lead to significant variability in precipitation [57].

For statistical analysis, the ADF test was conducted to assess the stationarity of the precipitation data for each city. Following this, the MK test was employed to identify and evaluate the significance of any trends present. The results of these tests are presented in

Table 3. The ADF test, and MK trend test results.

City	N	ADF Test Statistic	Stationarity	MK Statistic	Standard Error	Z Value	Prob > |Z|	Alpha	Sgn	Linear Trend
Tehran	72	−7.22	Stationary	90	205.71	0.43	0.67	0.05	0	-
Mashhad	72	−6.78	Stationary	−102	205.71	−0.49	0.62	0.05	0	-
Isfahan	72	−6.23	Stationary	180	205.71	0.87	0.38	0.05	0	-
Karaj	38	−4.84	Stationary	−5	79.54	−0.05	0.96	0.05	0	-
Shiraz	72	−5.81	Stationary	−272	205.71	−1.32	0.19	0.05	0	-
Tabriz	72	−6.02	Stationary	−544	205.71	−2.64	0.01	0.05	1	Downward

. This table indicates that the precipitation data for all cities were found to be stationary. In addition, at the 95% confidence level, only Tabriz exhibited a statistically significant trend, showing a reduction in precipitation. Nonetheless, when examining other confidence intervals, the Z values indicated different precipitation trends across various cities. For instance, Tehran and Isfahan displayed increasing trends, while Mashhad, Karaj, and Shiraz showed declining trends. These diverse outcomes imply that precipitation patterns might be affected by numerous local and regional factors, including geography, urban development, and atmospheric conditions.

In the next phase of the study, a detailed analysis was conducted to compare observed precipitation data with historical daily outputs from the GCMs. The purpose of this comparison was to assess the accuracy of the GCMs in reflecting real-world observations of precipitation patterns in the cities being examined. The primary goal of this comparative analysis was to pinpoint which GCMs most effectively resembled the observed precipitation patterns.

To evaluate the accuracy of the GCMs’ simulations against the actual observed data and recognize the inherent uncertainties that typically accompany precipitation simulations, the MNS efficiency coefficient was employed with the parameter j set to 1, in accordance with Equation (9). The results of this comprehensive comparison are presented in

Table 4. The MNS efficiency coefficient values for observed vs. simulated data.

GCM	Tehran	Karaj	Tabriz	Mashhad	Isfahan	Shiraz
ACCESS-CM2	0.18	0.10	−0.11	0.18	−0.09	0.21
ACCESS-ESM1-5	0.20	0.15	−0.10	0.20	0.01	0.25
BCC-CSM2-MR	0.18	0.11	−0.10	0.18	−0.06	0.22
CanESM5	0.19	0.08	−0.06	0.19	−0.05	0.20
CESM2	−0.37	−0.40	−0.66	−0.49	−0.53	−0.27
CESM2-WACCM	−0.34	−0.42	−0.66	−0.46	−0.50	−0.26
CMCC-CM2-SR5	0.11	0.09	−0.14	0.14	−0.15	0.12
CMCC-ESM2	0.16	0.12	−0.14	0.08	−0.07	0.13
CNRM-CM6-1	0.20	0.13	0	0.21	0.01	0.26
CNRM-ESM2-1	0.24	0.12	−0.10	0.21	−0.06	0.21
EC-Earth3	0.13	0.03	−0.15	0.12	−0.02	0.19
EC-Earth3-Veg-LR	0.13	0.09	−0.15	0.14	−0.06	0.18
FGOALS-g3	0.15	0.13	−0.06	0.17	−0.02	0.15
GFDL-CM4	0.12	0.04	−0.18	0.11	−0.06	0.20
GFDL-CM4_gr2	0.14	0.07	−0.13	0.14	−0.04	0.20
GFDL-ESM4	0.14	0.07	−0.16	0.16	−0.07	0.21
GISS-E2-1-G	0.21	0.16	−0.07	0.23	0.00	0.21
HadGEM3-GC31-LL	−0.37	−0.54	−0.53	−0.42	−0.57	−0.24
HadGEM3-GC31-MM	−0.33	−0.51	−0.52	−0.38	−0.53	−0.21
IITM-ESM	0.17	0.06	−0.11	0.20	−0.04	0.22
INM-CM4-8	0.10	0.00	−0.15	0.16	−0.06	0.15
INM-CM5-0	0.15	0.11	−0.14	0.17	0.01	0.15
IPSL-CM6A-LR	0.20	0.16	−0.08	0.23	−0.01	0.19
KACE-1-0-G	−0.18	−0.36	−0.39	−0.31	−0.82	−0.26
KIOST-ESM	0.20	0.14	−0.08	0.19	−0.07	0.22
MIROC6	0.18	0.08	−0.10	0.18	−0.06	0.17
MIROC-ES2L	0.25	0.12	−0.07	0.28	0.02	0.21
MPI-ESM1-2-HR	0.11	0.04	−0.18	0.14	−0.03	0.17
MPI-ESM1-2-LR	0.16	0.07	−0.14	0.12	−0.12	0.14
MRI-ESM2-0	0.19	0.07	−0.07	0.18	−0.01	0.25
NESM3	0.17	0.07	−0.15	0.10	−0.15	0.12
NorESM2-LM	−0.33	−0.42	−0.61	−0.44	−0.55	−0.30
NorESM2-MM	−0.36	−0.36	−0.61	−0.46	−0.52	−0.27
TaiESM1	−0.37	−0.47	−0.62	−0.50	−0.57	−0.29
UKESM1-0-LL	−0.35	−0.53	−0.51	−0.39	−0.58	−0.24

. High-efficiency values, which signify a good match with the observed data, are highlighted in green. Within the comprehensive set of 35 GCMs analyzed, the models that showed the greatest alignment with the observed data in terms of precipitation patterns included: MIROC-ES2L for Tehran, Mashhad, and Isfahan; GISS-E2-1-G for Karaj; and CNRM-CM6-1 for Tabriz and Shiraz. These GCMs were chosen for future climate projections to identify the number of dry days and very heavy precipitation days in each city. The models that underperformed were excluded from further analyses. This careful selection of GCMs ensures that future climate projections are based on a reliable and accurate empirical foundation. This is particularly important for developing strategies to address and mitigate the impacts of climate change on Iran’s key urban areas.

The GCMs selected for this study have been widely utilized by researchers globally for future climate studies. For instance, Babiker et al. (2024) [58], Hoseini et al. (2024) [59], as well as Xiao et al. (2023) [60] all employed the MIROC-ES2L model for climate change studies; Nazarenko et al. (2022) used the GISS-E2-1-G model in their research [61], as did Sun et al. (2022) [62], and Romanou et al. (2020) [63]; the CNRM-CM6-1 model was utilized by Nooni et al. (2022) [64], Wang et al. (2021) [65], and Séférian et al. (2019) [66].

In the next step, the selected GCMs were used to forecast precipitation patterns for each city from 2025 to 2100 under various scenarios (Figure 3). To gain a clearer understanding of the precipitation extremes depicted in Figure 3, boxplots were employed to illustrate the data distribution (Figure 4).

The findings for Tehran indicate significant year-to-year variability in precipitation across all SSPs. SSP585 generally shows higher precipitation towards the end of the century, while SSP126 tends to have lower values. The median precipitation increases from SSP126 to SSP585, with SSP126 having the lowest median and a more compact distribution.

In Mashhad, the pattern of annual variability is similar, with SSP585 showing higher peaks towards the later years. Other SSP scenarios (SSP126, SSP245, and SSP370) exhibit lower trends compared to SSP585. The median precipitation is relatively similar across SSP245, SSP370, and SSP585, whereas SSP126 has a noticeably lower median and tighter distribution.

Isfahan shows consistent variability across all SSPs, with notable peaks and troughs. SSP585 exhibits higher precipitation values, especially in the later years. The median values are similar across all SSP scenarios, with SSP126 having a more compact distribution and the others being more spread out. Outliers are present in SSP245 and SSP370.

In Karaj, significant inter-annual variability in precipitation is observed, with SSP585 consistently showing higher values compared to other scenarios. The median precipitation is fairly consistent across all scenarios, although SSP126 shows a slightly lower median. The distribution is similar across all scenarios, with a few outliers, particularly in SSP245 and SSP370.

Shiraz exhibits a high degree of variability, with frequent peaks in precipitation under all scenarios. SSP585 shows the highest values, particularly after 2050. The median values are similar across all SSPs, with SSP126 showing slightly lower values and a more compact distribution. SSP245, SSP370, and SSP585 have a wider spread with higher outliers, especially in SSP245 and SSP370.

Tabriz shows similar patterns of variability, with SSP585 exhibiting higher values. Other SSP scenarios (SSP126, SSP245, and SSP370) demonstrate lower and relatively consistent trends. The median precipitation is consistent across scenarios, with SSP126 showing slightly lower median values. SSP245, SSP370, and SSP585 have similar distributions with a few high outliers.

According to Figure 3 and Figure 4, projections for all cities show that SSP585 consistently predicts higher annual precipitation, particularly towards the latter half of the century, under this high-emission scenario. All scenarios exhibit significant year-to-year variability, underscoring the challenge of accurately forecasting future precipitation patterns. SSP126 generally presents lower precipitation values compared to higher emission scenarios, suggesting that lower emissions could result in reduced annual precipitation. These findings indicate that higher emission pathways may lead to increased and more variable precipitation, with important implications for urban planning and climate adaptation strategies.

Furthermore, SSP126 typically shows lower median precipitation and narrower distributions compared to other scenarios. In contrast, higher SSP scenarios (SSP245, SSP370, and SSP585) demonstrate higher median precipitation and greater variability, suggesting increased precipitation under more intense scenarios. The presence of high outliers, especially in SSP245 and SSP370, points to potential extreme precipitation events. The analysis indicates that as the SSP scenario intensifies, both the median precipitation and annual variability tend to increase, potentially signaling more extreme weather patterns. These findings align with those reported by Naderi et al. (2024) [67]. Evaluating data from 1980 to 2014 and projections under SSP119, SSP245, and SSP585 for 2021–2080, they also reported that higher emission scenarios lead to increased precipitation and variability.

Moreover, an ADF stationarity test and MK analysis were conducted on the results to identify future precipitation trends. According to

Table 5. The ADF test and the MK trend test results for forecasted precipitation in each city.

City	Scenario	N	ADF Test Statistic	Stationarity	M–K Statistic	Standard Error	Z Value	Prob > |Z|	Alpha	Sgn	Trend
Tehran	SSP126	76	−8.89	Stationary	8	222.97235	0.03139	0.97496	0.05	0	-
	SSP245	76	−7.66	Stationary	−314	222.97235	−1.40376	0.16039	0.05	0	-
	SSP370	76	−8.01	Stationary	320	222.97235	1.43067	0.15252	0.05	0	-
	SSP585	76	−8.04	Stationary	12	222.97235	0.04933	0.96065	0.05	0	-
Mashhad	SSP126	76	−8.68	Stationary	−190	222.97235	−0.84764	0.39664	0.05	0	-
	SSP245	76	−8.60	Stationary	74	222.97235	0.32739	0.74337	0.05	0	-
	SSP370	76	−3.49	Stationary	452	222.97235	2.02267	0.04311	0.05	1	Upward
	SSP585	76	−7.82	Stationary	60	222.97235	0.26461	0.79131	0.05	0	-
Isfahan	SSP126	76	−9.00	Stationary	−56	222.97235	−0.24667	0.80517	0.05	0	-
	SSP245	76	−8.59	Stationary	0	222.97235	0	1	0.05	0	-
	SSP370	76	−8.32	Stationary	204	222.97235	0.91043	0.3626	0.05	0	-
	SSP585	76	−7.45	Stationary	0	222.97235	0	1	0.05	0	-
Karaj	SSP126	76	−7.35	Stationary	−38	222.97235	−0.16594	0.8682	0.05	0	-
	SSP245	76	−8.58	Stationary	84	222.97235	0.37224	0.70971	0.05	0	-
	SSP370	76	−9.25	Stationary	518	222.97235	2.31867	0.02041	0.05	1	Upward
	SSP585	76	−9.18	Stationary	292	222.97235	1.30509	0.19186	0.05	0	-
Shiraz	SSP126	76	−3.61	Stationary	−58	222.97235	−0.25564	0.79823	0.05	0	-
	SSP245	76	−8.29	Stationary	−54	222.97235	−0.2377	0.81212	0.05	0	-
	SSP370	76	−9.13	Stationary	−132	222.97235	−0.58752	0.55686	0.05	0	-
	SSP585	76	−8.30	Stationary	40	222.97235	0.17491	0.86115	0.05	0	-
Tabriz	SSP126	76	−6.62	Stationary	84	222.97235	0.37224	0.70971	0.05	0	-
	SSP245	76	−7.80	Stationary	400	222.97235	1.78946	0.07354	0.05	0	-
	SSP370	76	−7.66	Stationary	8	222.97235	0.03139	0.97496	0.05	0	-
	SSP585	76	−4.22	Stationary	−24	222.97235	−0.10315	0.91784	0.05	0	-

, at a 95% confidence interval, Mashhad and Karaj show significant trends under the SSP370 scenario. Tehran, Isfahan, and Shiraz show no significant trends in any scenario. However, Tabriz shows no significant trends, but SSP245 approaches significance.

In the last step, based on the forecasted precipitation data, the number of dry days and very heavy precipitation days were identified for each city, under different scenarios. According to

Table 6. Number of dry days and very heavy precipitation days in each city.

City	Number of Dry Days				Number of Very Heavy Precipitation Days
	SSP126	SSP245	SSP370	SSP585	SSP126	SSP245	SSP370	SSP585
Tehran	23,577	23,310	23,388	23,609	203	302	257	258
Mashhad	23,946	23,705	23,512	23,813	408	494	550	529
Isfahan	24,530	24,064	24,107	24,315	190	240	245	232
Karaj	22,255	22,372	22,119	22,091	376	376	401	419
Shiraz	25,062	25,040	25,069	25,138	728	698	778	740
Tabriz	20,831	20,952	21,336	21,375	403	413	438	485

, across all cities, SSP126 generally results in the highest number of dry days, indicating potentially less frequent but intense precipitation events under lower emission scenarios. SSP585 generally results in the lowest number of dry days. On the other hand, higher emission scenarios (SSP370, SSP585) consistently show an increase in the number of very heavy precipitation days across all cities, indicating a trend towards more extreme weather events as emissions increase. Overall, the data suggests that higher emission scenarios are associated with fewer dry days and more very heavy precipitation days, highlighting the potential for increased precipitation extremes with climate change.

The comparison between SSP126 and SSP585 suggests that lower emissions are associated with more stable and predictable rainfall patterns. Therefore, to reduce carbon emissions and follow SSP126, it is recommended that the adoption of renewable energy sources such as solar, wind, and hydroelectric power be increased, energy efficiency measures be implemented across all sectors, sustainable transportation systems including public transport and electric vehicles be developed, carbon pricing mechanisms be implemented, forests be protected and expanded through afforestation and reforestation projects, sustainable agricultural practices be promoted, waste management systems be improved, green building codes be enforced, urban areas be designed to minimize energy-intensive transportation, public awareness and education on sustainability be increased, and international cooperation be enhanced to share technologies and best practices for reducing global emissions [68].

By providing a detailed analysis of the projected changes in the cumulative number of dry days and very heavy precipitation days from 2025 to 2100, this study can equip policymakers and urban planners with the information necessary to develop targeted and effective adaptation strategies. The findings of this study allow for the improvement of early warning systems by identifying cities more prone to heavy precipitation and drought conditions, enabling authorities to implement timely alerts and preparedness measures that reduce the risk of human and economic losses [69]. Understanding the future patterns of dry and very heavy precipitation days helps in designing better water resource management strategies, such as developing more efficient water storage and conservation techniques in regions with increasing dry days to ensure a stable water supply during prolonged dry periods [70]. The insights gained from this study can guide the planning and development of resilient infrastructure, enabling urban planners to design drainage systems and flood defenses capable of handling projected increases in very heavy precipitation, thereby reducing the risk of flooding and associated damage [71]. This research provides a scientific basis for formulating policies aimed at climate adaptation, allowing policymakers to develop and implement strategies tailored to the specific needs of different metropolises, enhancing their resilience to extreme weather events. Additionally, by highlighting the potential impacts of climate change on precipitation patterns, this study can raise public awareness and encourage community involvement in disaster risk reduction and drought mitigation efforts, fostering a culture of preparedness and resilience [72].

4. Conclusions

This study utilized a comprehensive methodological strategy to examine the future climate conditions of six Iranian metropolises, employing 35 GCMs from the CMIP6 series to forecast precipitation patterns from 2025 to 2100. The primary focus was on identifying trends in the number of dry days and very heavy precipitation days. After evaluating the accuracy of the models against historical data, MIROC-ES2L, GISS-E2-1-G, and CNRM-CM6-1 were selected for detailed projections under four scenarios: SSP126, SSP245, SSP370, and SSP585.

The general findings indicate that the SSP585 scenario, representing high emissions, projects significantly higher annual precipitation across all cities, especially towards the latter half of the century. Conversely, the SSP126 scenario, representing low emissions, consistently shows reduced annual precipitation. The intermediate scenarios, SSP245 and SSP370, present moderate increases in precipitation with noticeable variability.

Significant trends were detected in specific cities; for instance, the MKMK analysis revealed notable trends in Mashhad and Karaj under the SSP370 scenario, while other cities exhibited less pronounced trends.

Overall, this study highlights the importance of selecting accurate GCMs and considering multiple emission scenarios to understand future precipitation patterns. Future research should focus on developing and evaluating adaptation strategies tailored to the specific precipitation trends and variability identified in each city, leveraging the latest projections from GCMs to enhance urban resilience against climate change.